------------------------------------------------------------------------
-- dqMultiply.decTest -- decQuad multiplication                       --
-- Copyright (c) IBM Corporation, 1981, 2008.  All rights reserved.   --
------------------------------------------------------------------------
-- Please see the document "General Decimal Arithmetic Testcases"     --
-- at http://www2.hursley.ibm.com/decimal for the description of      --
-- these testcases.                                                   --
--                                                                    --
-- These testcases are experimental ('beta' versions), and they       --
-- may contain errors.  They are offered on an as-is basis.  In       --
-- particular, achieving the same results as the tests here is not    --
-- a guarantee that an implementation complies with any Standard      --
-- or specification.  The tests are not exhaustive.                   --
--                                                                    --
-- Please send comments, suggestions, and corrections to the author:  --
--   Mike Cowlishaw, IBM Fellow                                       --
--   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         --
--   mfc@uk.ibm.com                                                   --
------------------------------------------------------------------------
version: 2.59

-- This set of tests are for decQuads only; all arguments are
-- representable in a decQuad
extended:    1
clamp:       1
precision:   34
maxExponent: 6144
minExponent: -6143
rounding:    half_even

-- sanity checks
dqmul000 multiply 2      2 -> 4
dqmul001 multiply 2      3 -> 6
dqmul002 multiply 5      1 -> 5
dqmul003 multiply 5      2 -> 10
dqmul004 multiply 1.20   2 -> 2.40
dqmul005 multiply 1.20   0 -> 0.00
dqmul006 multiply 1.20  -2 -> -2.40
dqmul007 multiply -1.20  2 -> -2.40
dqmul008 multiply -1.20  0 -> -0.00
dqmul009 multiply -1.20 -2 -> 2.40
dqmul010 multiply 5.09 7.1 -> 36.139
dqmul011 multiply 2.5    4 -> 10.0
dqmul012 multiply 2.50   4 -> 10.00
dqmul013 multiply 1.23456789 1.0000000000000000000000000000 -> 1.234567890000000000000000000000000 Rounded
dqmul015 multiply 2.50   4 -> 10.00
dqmul016 multiply  9.99999999999999999  9.99999999999999999 ->  99.99999999999999980000000000000000 Inexact Rounded
dqmul017 multiply  9.99999999999999999 -9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded
dqmul018 multiply -9.99999999999999999  9.99999999999999999 -> -99.99999999999999980000000000000000 Inexact Rounded
dqmul019 multiply -9.99999999999999999 -9.99999999999999999 ->  99.99999999999999980000000000000000 Inexact Rounded

-- zeros, etc.
dqmul021 multiply  0      0     ->  0
dqmul022 multiply  0     -0     -> -0
dqmul023 multiply -0      0     -> -0
dqmul024 multiply -0     -0     ->  0
dqmul025 multiply -0.0   -0.0   ->  0.00
dqmul026 multiply -0.0   -0.0   ->  0.00
dqmul027 multiply -0.0   -0.0   ->  0.00
dqmul028 multiply -0.0   -0.0   ->  0.00
dqmul030 multiply  5.00   1E-3  ->  0.00500
dqmul031 multiply  00.00  0.000 ->  0.00000
dqmul032 multiply  00.00  0E-3  ->  0.00000     -- rhs is 0
dqmul033 multiply  0E-3   00.00 ->  0.00000     -- lhs is 0
dqmul034 multiply -5.00   1E-3  -> -0.00500
dqmul035 multiply -00.00  0.000 -> -0.00000
dqmul036 multiply -00.00  0E-3  -> -0.00000     -- rhs is 0
dqmul037 multiply -0E-3   00.00 -> -0.00000     -- lhs is 0
dqmul038 multiply  5.00  -1E-3  -> -0.00500
dqmul039 multiply  00.00 -0.000 -> -0.00000
dqmul040 multiply  00.00 -0E-3  -> -0.00000     -- rhs is 0
dqmul041 multiply  0E-3  -00.00 -> -0.00000     -- lhs is 0
dqmul042 multiply -5.00  -1E-3  ->  0.00500
dqmul043 multiply -00.00 -0.000 ->  0.00000
dqmul044 multiply -00.00 -0E-3  ->  0.00000     -- rhs is 0
dqmul045 multiply -0E-3  -00.00 ->  0.00000     -- lhs is 0

-- examples from decarith
dqmul050 multiply 1.20 3        -> 3.60
dqmul051 multiply 7    3        -> 21
dqmul052 multiply 0.9  0.8      -> 0.72
dqmul053 multiply 0.9  -0       -> -0.0
dqmul054 multiply 654321 654321 -> 428135971041

dqmul060 multiply 123.45 1e7  ->  1.2345E+9
dqmul061 multiply 123.45 1e8  ->  1.2345E+10
dqmul062 multiply 123.45 1e+9 ->  1.2345E+11
dqmul063 multiply 123.45 1e10 ->  1.2345E+12
dqmul064 multiply 123.45 1e11 ->  1.2345E+13
dqmul065 multiply 123.45 1e12 ->  1.2345E+14
dqmul066 multiply 123.45 1e13 ->  1.2345E+15


-- test some intermediate lengths
--                    1234567890123456
dqmul080 multiply 0.1 1230123456456789     -> 123012345645678.9
dqmul084 multiply 0.1 1230123456456789     -> 123012345645678.9
dqmul090 multiply 1230123456456789     0.1 -> 123012345645678.9
dqmul094 multiply 1230123456456789     0.1 -> 123012345645678.9

-- test some more edge cases and carries
dqmul101 multiply 9 9   -> 81
dqmul102 multiply 9 90   -> 810
dqmul103 multiply 9 900   -> 8100
dqmul104 multiply 9 9000   -> 81000
dqmul105 multiply 9 90000   -> 810000
dqmul106 multiply 9 900000   -> 8100000
dqmul107 multiply 9 9000000   -> 81000000
dqmul108 multiply 9 90000000   -> 810000000
dqmul109 multiply 9 900000000   -> 8100000000
dqmul110 multiply 9 9000000000   -> 81000000000
dqmul111 multiply 9 90000000000   -> 810000000000
dqmul112 multiply 9 900000000000   -> 8100000000000
dqmul113 multiply 9 9000000000000   -> 81000000000000
dqmul114 multiply 9 90000000000000   -> 810000000000000
dqmul115 multiply 9 900000000000000   -> 8100000000000000
--dqmul116 multiply 9 9000000000000000   -> 81000000000000000
--dqmul117 multiply 9 90000000000000000   -> 810000000000000000
--dqmul118 multiply 9 900000000000000000   -> 8100000000000000000
--dqmul119 multiply 9 9000000000000000000   -> 81000000000000000000
--dqmul120 multiply 9 90000000000000000000   -> 810000000000000000000
--dqmul121 multiply 9 900000000000000000000   -> 8100000000000000000000
--dqmul122 multiply 9 9000000000000000000000   -> 81000000000000000000000
--dqmul123 multiply 9 90000000000000000000000   -> 810000000000000000000000
-- test some more edge cases without carries
dqmul131 multiply 3 3   -> 9
dqmul132 multiply 3 30   -> 90
dqmul133 multiply 3 300   -> 900
dqmul134 multiply 3 3000   -> 9000
dqmul135 multiply 3 30000   -> 90000
dqmul136 multiply 3 300000   -> 900000
dqmul137 multiply 3 3000000   -> 9000000
dqmul138 multiply 3 30000000   -> 90000000
dqmul139 multiply 3 300000000   -> 900000000
dqmul140 multiply 3 3000000000   -> 9000000000
dqmul141 multiply 3 30000000000   -> 90000000000
dqmul142 multiply 3 300000000000   -> 900000000000
dqmul143 multiply 3 3000000000000   -> 9000000000000
dqmul144 multiply 3 30000000000000   -> 90000000000000
dqmul145 multiply 3 300000000000000   -> 900000000000000
dqmul146 multiply 3 3000000000000000   -> 9000000000000000
dqmul147 multiply 3 30000000000000000   -> 90000000000000000
dqmul148 multiply 3 300000000000000000   -> 900000000000000000
dqmul149 multiply 3 3000000000000000000   -> 9000000000000000000
dqmul150 multiply 3 30000000000000000000   -> 90000000000000000000
dqmul151 multiply 3 300000000000000000000   -> 900000000000000000000
dqmul152 multiply 3 3000000000000000000000   -> 9000000000000000000000
dqmul153 multiply 3 30000000000000000000000   -> 90000000000000000000000

dqmul263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928296 Inexact Rounded

-- test some edge cases with exact rounding
dqmul301 multiply 900000000000000000 9   -> 8100000000000000000
dqmul302 multiply 900000000000000000 90   -> 81000000000000000000
dqmul303 multiply 900000000000000000 900   -> 810000000000000000000
dqmul304 multiply 900000000000000000 9000   -> 8100000000000000000000
dqmul305 multiply 900000000000000000 90000   -> 81000000000000000000000
dqmul306 multiply 900000000000000000 900000   -> 810000000000000000000000
dqmul307 multiply 900000000000000000 9000000   -> 8100000000000000000000000
dqmul308 multiply 900000000000000000 90000000   -> 81000000000000000000000000
dqmul309 multiply 900000000000000000 900000000   -> 810000000000000000000000000
dqmul310 multiply 900000000000000000 9000000000   -> 8100000000000000000000000000
dqmul311 multiply 900000000000000000 90000000000   -> 81000000000000000000000000000
dqmul312 multiply 900000000000000000 900000000000   -> 810000000000000000000000000000
dqmul313 multiply 900000000000000000 9000000000000   -> 8100000000000000000000000000000
dqmul314 multiply 900000000000000000 90000000000000   -> 81000000000000000000000000000000
dqmul315 multiply 900000000000000000 900000000000000   -> 810000000000000000000000000000000
dqmul316 multiply 900000000000000000 9000000000000000   -> 8100000000000000000000000000000000
dqmul317 multiply 9000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+34  Rounded
dqmul318 multiply 90000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+35  Rounded
dqmul319 multiply 900000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+36  Rounded
dqmul320 multiply 9000000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+37  Rounded
dqmul321 multiply 90000000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+38  Rounded
dqmul322 multiply 900000000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+39  Rounded
dqmul323 multiply 9000000000000000000000000 9000000000000000   -> 8.100000000000000000000000000000000E+40  Rounded

-- tryzeros cases
dqmul504  multiply  0E-4260 1000E-4260  -> 0E-6176 Clamped
dqmul505  multiply  100E+4260 0E+4260   -> 0E+6111 Clamped

-- mixed with zeros
dqmul541 multiply  0    -1     -> -0
dqmul542 multiply -0    -1     ->  0
dqmul543 multiply  0     1     ->  0
dqmul544 multiply -0     1     -> -0
dqmul545 multiply -1     0     -> -0
dqmul546 multiply -1    -0     ->  0
dqmul547 multiply  1     0     ->  0
dqmul548 multiply  1    -0     -> -0

dqmul551 multiply  0.0  -1     -> -0.0
dqmul552 multiply -0.0  -1     ->  0.0
dqmul553 multiply  0.0   1     ->  0.0
dqmul554 multiply -0.0   1     -> -0.0
dqmul555 multiply -1.0   0     -> -0.0
dqmul556 multiply -1.0  -0     ->  0.0
dqmul557 multiply  1.0   0     ->  0.0
dqmul558 multiply  1.0  -0     -> -0.0

dqmul561 multiply  0    -1.0   -> -0.0
dqmul562 multiply -0    -1.0   ->  0.0
dqmul563 multiply  0     1.0   ->  0.0
dqmul564 multiply -0     1.0   -> -0.0
dqmul565 multiply -1     0.0   -> -0.0
dqmul566 multiply -1    -0.0   ->  0.0
dqmul567 multiply  1     0.0   ->  0.0
dqmul568 multiply  1    -0.0   -> -0.0

dqmul571 multiply  0.0  -1.0   -> -0.00
dqmul572 multiply -0.0  -1.0   ->  0.00
dqmul573 multiply  0.0   1.0   ->  0.00
dqmul574 multiply -0.0   1.0   -> -0.00
dqmul575 multiply -1.0   0.0   -> -0.00
dqmul576 multiply -1.0  -0.0   ->  0.00
dqmul577 multiply  1.0   0.0   ->  0.00
dqmul578 multiply  1.0  -0.0   -> -0.00


-- Specials
dqmul580 multiply  Inf  -Inf   -> -Infinity
dqmul581 multiply  Inf  -1000  -> -Infinity
dqmul582 multiply  Inf  -1     -> -Infinity
dqmul583 multiply  Inf  -0     ->  NaN  Invalid_operation
dqmul584 multiply  Inf   0     ->  NaN  Invalid_operation
dqmul585 multiply  Inf   1     ->  Infinity
dqmul586 multiply  Inf   1000  ->  Infinity
dqmul587 multiply  Inf   Inf   ->  Infinity
dqmul588 multiply -1000  Inf   -> -Infinity
dqmul589 multiply -Inf   Inf   -> -Infinity
dqmul590 multiply -1     Inf   -> -Infinity
dqmul591 multiply -0     Inf   ->  NaN  Invalid_operation
dqmul592 multiply  0     Inf   ->  NaN  Invalid_operation
dqmul593 multiply  1     Inf   ->  Infinity
dqmul594 multiply  1000  Inf   ->  Infinity
dqmul595 multiply  Inf   Inf   ->  Infinity

dqmul600 multiply -Inf  -Inf   ->  Infinity
dqmul601 multiply -Inf  -1000  ->  Infinity
dqmul602 multiply -Inf  -1     ->  Infinity
dqmul603 multiply -Inf  -0     ->  NaN  Invalid_operation
dqmul604 multiply -Inf   0     ->  NaN  Invalid_operation
dqmul605 multiply -Inf   1     -> -Infinity
dqmul606 multiply -Inf   1000  -> -Infinity
dqmul607 multiply -Inf   Inf   -> -Infinity
dqmul608 multiply -1000  Inf   -> -Infinity
dqmul609 multiply -Inf  -Inf   ->  Infinity
dqmul610 multiply -1    -Inf   ->  Infinity
dqmul611 multiply -0    -Inf   ->  NaN  Invalid_operation
dqmul612 multiply  0    -Inf   ->  NaN  Invalid_operation
dqmul613 multiply  1    -Inf   -> -Infinity
dqmul614 multiply  1000 -Inf   -> -Infinity
dqmul615 multiply  Inf  -Inf   -> -Infinity

dqmul621 multiply  NaN -Inf    ->  NaN
dqmul622 multiply  NaN -1000   ->  NaN
dqmul623 multiply  NaN -1      ->  NaN
dqmul624 multiply  NaN -0      ->  NaN
dqmul625 multiply  NaN  0      ->  NaN
dqmul626 multiply  NaN  1      ->  NaN
dqmul627 multiply  NaN  1000   ->  NaN
dqmul628 multiply  NaN  Inf    ->  NaN
dqmul629 multiply  NaN  NaN    ->  NaN
dqmul630 multiply -Inf  NaN    ->  NaN
dqmul631 multiply -1000 NaN    ->  NaN
dqmul632 multiply -1    NaN    ->  NaN
dqmul633 multiply -0    NaN    ->  NaN
dqmul634 multiply  0    NaN    ->  NaN
dqmul635 multiply  1    NaN    ->  NaN
dqmul636 multiply  1000 NaN    ->  NaN
dqmul637 multiply  Inf  NaN    ->  NaN

dqmul641 multiply  sNaN -Inf   ->  NaN  Invalid_operation
dqmul642 multiply  sNaN -1000  ->  NaN  Invalid_operation
dqmul643 multiply  sNaN -1     ->  NaN  Invalid_operation
dqmul644 multiply  sNaN -0     ->  NaN  Invalid_operation
dqmul645 multiply  sNaN  0     ->  NaN  Invalid_operation
dqmul646 multiply  sNaN  1     ->  NaN  Invalid_operation
dqmul647 multiply  sNaN  1000  ->  NaN  Invalid_operation
dqmul648 multiply  sNaN  NaN   ->  NaN  Invalid_operation
dqmul649 multiply  sNaN sNaN   ->  NaN  Invalid_operation
dqmul650 multiply  NaN  sNaN   ->  NaN  Invalid_operation
dqmul651 multiply -Inf  sNaN   ->  NaN  Invalid_operation
dqmul652 multiply -1000 sNaN   ->  NaN  Invalid_operation
dqmul653 multiply -1    sNaN   ->  NaN  Invalid_operation
dqmul654 multiply -0    sNaN   ->  NaN  Invalid_operation
dqmul655 multiply  0    sNaN   ->  NaN  Invalid_operation
dqmul656 multiply  1    sNaN   ->  NaN  Invalid_operation
dqmul657 multiply  1000 sNaN   ->  NaN  Invalid_operation
dqmul658 multiply  Inf  sNaN   ->  NaN  Invalid_operation
dqmul659 multiply  NaN  sNaN   ->  NaN  Invalid_operation

-- propagating NaNs
dqmul661 multiply  NaN9 -Inf   ->  NaN9
dqmul662 multiply  NaN8  999   ->  NaN8
dqmul663 multiply  NaN71 Inf   ->  NaN71
dqmul664 multiply  NaN6  NaN5  ->  NaN6
dqmul665 multiply -Inf   NaN4  ->  NaN4
dqmul666 multiply -999   NaN33 ->  NaN33
dqmul667 multiply  Inf   NaN2  ->  NaN2

dqmul671 multiply  sNaN99 -Inf    ->  NaN99 Invalid_operation
dqmul672 multiply  sNaN98 -11     ->  NaN98 Invalid_operation
dqmul673 multiply  sNaN97  NaN    ->  NaN97 Invalid_operation
dqmul674 multiply  sNaN16 sNaN94  ->  NaN16 Invalid_operation
dqmul675 multiply  NaN95  sNaN93  ->  NaN93 Invalid_operation
dqmul676 multiply -Inf    sNaN92  ->  NaN92 Invalid_operation
dqmul677 multiply  088    sNaN91  ->  NaN91 Invalid_operation
dqmul678 multiply  Inf    sNaN90  ->  NaN90 Invalid_operation
dqmul679 multiply  NaN    sNaN89  ->  NaN89 Invalid_operation

dqmul681 multiply -NaN9 -Inf   -> -NaN9
dqmul682 multiply -NaN8  999   -> -NaN8
dqmul683 multiply -NaN71 Inf   -> -NaN71
dqmul684 multiply -NaN6 -NaN5  -> -NaN6
dqmul685 multiply -Inf  -NaN4  -> -NaN4
dqmul686 multiply -999  -NaN33 -> -NaN33
dqmul687 multiply  Inf  -NaN2  -> -NaN2

dqmul691 multiply -sNaN99 -Inf    -> -NaN99 Invalid_operation
dqmul692 multiply -sNaN98 -11     -> -NaN98 Invalid_operation
dqmul693 multiply -sNaN97  NaN    -> -NaN97 Invalid_operation
dqmul694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation
dqmul695 multiply -NaN95  -sNaN93 -> -NaN93 Invalid_operation
dqmul696 multiply -Inf    -sNaN92 -> -NaN92 Invalid_operation
dqmul697 multiply  088    -sNaN91 -> -NaN91 Invalid_operation
dqmul698 multiply  Inf    -sNaN90 -> -NaN90 Invalid_operation
dqmul699 multiply -NaN    -sNaN89 -> -NaN89 Invalid_operation

dqmul701 multiply -NaN  -Inf   -> -NaN
dqmul702 multiply -NaN   999   -> -NaN
dqmul703 multiply -NaN   Inf   -> -NaN
dqmul704 multiply -NaN  -NaN   -> -NaN
dqmul705 multiply -Inf  -NaN0  -> -NaN
dqmul706 multiply -999  -NaN   -> -NaN
dqmul707 multiply  Inf  -NaN   -> -NaN

dqmul711 multiply -sNaN   -Inf    -> -NaN Invalid_operation
dqmul712 multiply -sNaN   -11     -> -NaN Invalid_operation
dqmul713 multiply -sNaN00  NaN    -> -NaN Invalid_operation
dqmul714 multiply -sNaN   -sNaN   -> -NaN Invalid_operation
dqmul715 multiply -NaN    -sNaN   -> -NaN Invalid_operation
dqmul716 multiply -Inf    -sNaN   -> -NaN Invalid_operation
dqmul717 multiply  088    -sNaN   -> -NaN Invalid_operation
dqmul718 multiply  Inf    -sNaN   -> -NaN Invalid_operation
dqmul719 multiply -NaN    -sNaN   -> -NaN Invalid_operation

-- overflow and underflow tests .. note subnormal results
-- signs
dqmul751 multiply  1e+4277  1e+3311 ->  Infinity Overflow Inexact Rounded
dqmul752 multiply  1e+4277 -1e+3311 -> -Infinity Overflow Inexact Rounded
dqmul753 multiply -1e+4277  1e+3311 -> -Infinity Overflow Inexact Rounded
dqmul754 multiply -1e+4277 -1e+3311 ->  Infinity Overflow Inexact Rounded
dqmul755 multiply  1e-4277  1e-3311 ->  0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul756 multiply  1e-4277 -1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul757 multiply -1e-4277  1e-3311 -> -0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul758 multiply -1e-4277 -1e-3311 ->  0E-6176 Underflow Subnormal Inexact Rounded Clamped

-- 'subnormal' boundary (all hard underflow or overflow in base arithemtic)
dqmul760 multiply 1e-6069 1e-101 -> 1E-6170 Subnormal
dqmul761 multiply 1e-6069 1e-102 -> 1E-6171 Subnormal
dqmul762 multiply 1e-6069 1e-103 -> 1E-6172 Subnormal
dqmul763 multiply 1e-6069 1e-104 -> 1E-6173 Subnormal
dqmul764 multiply 1e-6069 1e-105 -> 1E-6174 Subnormal
dqmul765 multiply 1e-6069 1e-106 -> 1E-6175 Subnormal
dqmul766 multiply 1e-6069 1e-107 -> 1E-6176 Subnormal
dqmul767 multiply 1e-6069 1e-108 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul768 multiply 1e-6069 1e-109 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul769 multiply 1e-6069 1e-110 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
-- [no equivalent of 'subnormal' for overflow]
dqmul770 multiply 1e+40 1e+6101 -> 1.000000000000000000000000000000E+6141 Clamped
dqmul771 multiply 1e+40 1e+6102 -> 1.0000000000000000000000000000000E+6142  Clamped
dqmul772 multiply 1e+40 1e+6103 -> 1.00000000000000000000000000000000E+6143  Clamped
dqmul773 multiply 1e+40 1e+6104 -> 1.000000000000000000000000000000000E+6144  Clamped
dqmul774 multiply 1e+40 1e+6105 -> Infinity Overflow Inexact Rounded
dqmul775 multiply 1e+40 1e+6106 -> Infinity Overflow Inexact Rounded
dqmul776 multiply 1e+40 1e+6107 -> Infinity Overflow Inexact Rounded
dqmul777 multiply 1e+40 1e+6108 -> Infinity Overflow Inexact Rounded
dqmul778 multiply 1e+40 1e+6109 -> Infinity Overflow Inexact Rounded
dqmul779 multiply 1e+40 1e+6110 -> Infinity Overflow Inexact Rounded

dqmul801 multiply  1.0000E-6172  1     -> 1.0000E-6172 Subnormal
dqmul802 multiply  1.000E-6172   1e-1  -> 1.000E-6173  Subnormal
dqmul803 multiply  1.00E-6172    1e-2  -> 1.00E-6174   Subnormal
dqmul804 multiply  1.0E-6172     1e-3  -> 1.0E-6175    Subnormal
dqmul805 multiply  1.0E-6172     1e-4  -> 1E-6176     Subnormal Rounded
dqmul806 multiply  1.3E-6172     1e-4  -> 1E-6176     Underflow Subnormal Inexact Rounded
dqmul807 multiply  1.5E-6172     1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul808 multiply  1.7E-6172     1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul809 multiply  2.3E-6172     1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul810 multiply  2.5E-6172     1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul811 multiply  2.7E-6172     1e-4  -> 3E-6176     Underflow Subnormal Inexact Rounded
dqmul812 multiply  1.49E-6172    1e-4  -> 1E-6176     Underflow Subnormal Inexact Rounded
dqmul813 multiply  1.50E-6172    1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul814 multiply  1.51E-6172    1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul815 multiply  2.49E-6172    1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul816 multiply  2.50E-6172    1e-4  -> 2E-6176     Underflow Subnormal Inexact Rounded
dqmul817 multiply  2.51E-6172    1e-4  -> 3E-6176     Underflow Subnormal Inexact Rounded

dqmul818 multiply  1E-6172       1e-4  -> 1E-6176     Subnormal
dqmul819 multiply  3E-6172       1e-5  -> 0E-6176     Underflow Subnormal Inexact Rounded Clamped
dqmul820 multiply  5E-6172       1e-5  -> 0E-6176     Underflow Subnormal Inexact Rounded Clamped
dqmul821 multiply  7E-6172       1e-5  -> 1E-6176     Underflow Subnormal Inexact Rounded
dqmul822 multiply  9E-6172       1e-5  -> 1E-6176     Underflow Subnormal Inexact Rounded
dqmul823 multiply  9.9E-6172     1e-5  -> 1E-6176     Underflow Subnormal Inexact Rounded

dqmul824 multiply  1E-6172      -1e-4  -> -1E-6176    Subnormal
dqmul825 multiply  3E-6172      -1e-5  -> -0E-6176    Underflow Subnormal Inexact Rounded Clamped
dqmul826 multiply -5E-6172       1e-5  -> -0E-6176    Underflow Subnormal Inexact Rounded Clamped
dqmul827 multiply  7E-6172      -1e-5  -> -1E-6176    Underflow Subnormal Inexact Rounded
dqmul828 multiply -9E-6172       1e-5  -> -1E-6176    Underflow Subnormal Inexact Rounded
dqmul829 multiply  9.9E-6172    -1e-5  -> -1E-6176    Underflow Subnormal Inexact Rounded
dqmul830 multiply  3.0E-6172    -1e-5  -> -0E-6176    Underflow Subnormal Inexact Rounded Clamped

dqmul831 multiply  1.0E-5977     1e-200 -> 0E-6176 Underflow Subnormal Inexact Rounded Clamped
dqmul832 multiply  1.0E-5977     1e-199 -> 1E-6176    Subnormal Rounded
dqmul833 multiply  1.0E-5977     1e-198 -> 1.0E-6175    Subnormal
dqmul834 multiply  2.0E-5977     2e-198 -> 4.0E-6175    Subnormal
dqmul835 multiply  4.0E-5977     4e-198 -> 1.60E-6174   Subnormal
dqmul836 multiply 10.0E-5977    10e-198 -> 1.000E-6173  Subnormal
dqmul837 multiply 30.0E-5977    30e-198 -> 9.000E-6173  Subnormal
dqmul838 multiply 40.0E-5982    40e-166 -> 1.6000E-6145 Subnormal
dqmul839 multiply 40.0E-5982    40e-165 -> 1.6000E-6144 Subnormal
dqmul840 multiply 40.0E-5982    40e-164 -> 1.6000E-6143

-- Long operand overflow may be a different path
dqmul870 multiply 100  9.999E+6143     ->  Infinity Inexact Overflow Rounded
dqmul871 multiply 100 -9.999E+6143     -> -Infinity Inexact Overflow Rounded
dqmul872 multiply      9.999E+6143 100 ->  Infinity Inexact Overflow Rounded
dqmul873 multiply     -9.999E+6143 100 -> -Infinity Inexact Overflow Rounded

-- check for double-rounded subnormals
dqmul881 multiply  1.2347E-6133 1.2347E-40  ->  1.524E-6173 Inexact Rounded Subnormal Underflow
dqmul882 multiply  1.234E-6133 1.234E-40    ->  1.523E-6173 Inexact Rounded Subnormal Underflow
dqmul883 multiply  1.23E-6133  1.23E-40     ->  1.513E-6173 Inexact Rounded Subnormal Underflow
dqmul884 multiply  1.2E-6133   1.2E-40      ->  1.44E-6173  Subnormal
dqmul885 multiply  1.2E-6133   1.2E-41      ->  1.44E-6174  Subnormal
dqmul886 multiply  1.2E-6133   1.2E-42      ->  1.4E-6175   Subnormal Inexact Rounded Underflow
dqmul887 multiply  1.2E-6133   1.3E-42      ->  1.6E-6175   Subnormal Inexact Rounded Underflow
dqmul888 multiply  1.3E-6133   1.3E-42      ->  1.7E-6175   Subnormal Inexact Rounded Underflow
dqmul889 multiply  1.3E-6133   1.3E-43      ->    2E-6176   Subnormal Inexact Rounded Underflow
dqmul890 multiply  1.3E-6134   1.3E-43      ->    0E-6176   Clamped Subnormal Inexact Rounded Underflow

dqmul891 multiply  1.2345E-39    1.234E-6133 ->  1.5234E-6172 Inexact Rounded Subnormal Underflow
dqmul892 multiply  1.23456E-39   1.234E-6133 ->  1.5234E-6172 Inexact Rounded Subnormal Underflow
dqmul893 multiply  1.2345E-40   1.234E-6133 ->  1.523E-6173  Inexact Rounded Subnormal Underflow
dqmul894 multiply  1.23456E-40  1.234E-6133 ->  1.523E-6173  Inexact Rounded Subnormal Underflow
dqmul895 multiply  1.2345E-41   1.234E-6133 ->  1.52E-6174   Inexact Rounded Subnormal Underflow
dqmul896 multiply  1.23456E-41  1.234E-6133 ->  1.52E-6174   Inexact Rounded Subnormal Underflow

-- Now explore the case where we get a normal result with Underflow
-- prove operands are exact
dqmul906 multiply  9.999999999999999999999999999999999E-6143  1                       -> 9.999999999999999999999999999999999E-6143
dqmul907 multiply                       1  0.09999999999999999999999999999999999     -> 0.09999999999999999999999999999999999
-- the next rounds to Nmin
dqmul908 multiply  9.999999999999999999999999999999999E-6143  0.09999999999999999999999999999999999     -> 1.000000000000000000000000000000000E-6143 Underflow Inexact Subnormal Rounded

-- hugest
dqmul909 multiply 9999999999999999999999999999999999 9999999999999999999999999999999999 -> 9.999999999999999999999999999999998E+67 Inexact Rounded
-- VG case
dqmul910 multiply 8.81125000000001349436E-1548 8.000000000000000000E-1550 -> 7.049000000000010795488000000000000E-3097 Rounded

-- Examples from SQL proposal (Krishna Kulkarni)
precision:   34
rounding:    half_up
maxExponent: 6144
minExponent: -6143
dqmul911  multiply 130E-2  120E-2 -> 1.5600
dqmul912  multiply 130E-2  12E-1  -> 1.560
dqmul913  multiply 130E-2  1E0    -> 1.30
dqmul914  multiply 1E2     1E4    -> 1E+6

-- power-of-ten edge cases
dqmul1001 multiply  1      10               -> 10
dqmul1002 multiply  1      100              -> 100
dqmul1003 multiply  1      1000             -> 1000
dqmul1004 multiply  1      10000            -> 10000
dqmul1005 multiply  1      100000           -> 100000
dqmul1006 multiply  1      1000000          -> 1000000
dqmul1007 multiply  1      10000000         -> 10000000
dqmul1008 multiply  1      100000000        -> 100000000
dqmul1009 multiply  1      1000000000       -> 1000000000
dqmul1010 multiply  1      10000000000      -> 10000000000
dqmul1011 multiply  1      100000000000     -> 100000000000
dqmul1012 multiply  1      1000000000000    -> 1000000000000
dqmul1013 multiply  1      10000000000000   -> 10000000000000
dqmul1014 multiply  1      100000000000000  -> 100000000000000
dqmul1015 multiply  1      1000000000000000 -> 1000000000000000

dqmul1016 multiply  1      1000000000000000000 -> 1000000000000000000
dqmul1017 multiply  1      100000000000000000000000000 -> 100000000000000000000000000
dqmul1018 multiply  1      1000000000000000000000000000 -> 1000000000000000000000000000
dqmul1019 multiply  1      10000000000000000000000000000 -> 10000000000000000000000000000
dqmul1020 multiply  1      1000000000000000000000000000000000 -> 1000000000000000000000000000000000

dqmul1021 multiply  10     1                -> 10
dqmul1022 multiply  10     10               -> 100
dqmul1023 multiply  10     100              -> 1000
dqmul1024 multiply  10     1000             -> 10000
dqmul1025 multiply  10     10000            -> 100000
dqmul1026 multiply  10     100000           -> 1000000
dqmul1027 multiply  10     1000000          -> 10000000
dqmul1028 multiply  10     10000000         -> 100000000
dqmul1029 multiply  10     100000000        -> 1000000000
dqmul1030 multiply  10     1000000000       -> 10000000000
dqmul1031 multiply  10     10000000000      -> 100000000000
dqmul1032 multiply  10     100000000000     -> 1000000000000
dqmul1033 multiply  10     1000000000000    -> 10000000000000
dqmul1034 multiply  10     10000000000000   -> 100000000000000
dqmul1035 multiply  10     100000000000000  -> 1000000000000000

dqmul1036 multiply  10     100000000000000000 -> 1000000000000000000
dqmul1037 multiply  10     10000000000000000000000000 -> 100000000000000000000000000
dqmul1038 multiply  10     100000000000000000000000000 -> 1000000000000000000000000000
dqmul1039 multiply  10     1000000000000000000000000000 -> 10000000000000000000000000000
dqmul1040 multiply  10     100000000000000000000000000000000 -> 1000000000000000000000000000000000

dqmul1041 multiply  100    0.1              -> 10.0
dqmul1042 multiply  100    1                -> 100
dqmul1043 multiply  100    10               -> 1000
dqmul1044 multiply  100    100              -> 10000
dqmul1045 multiply  100    1000             -> 100000
dqmul1046 multiply  100    10000            -> 1000000
dqmul1047 multiply  100    100000           -> 10000000
dqmul1048 multiply  100    1000000          -> 100000000
dqmul1049 multiply  100    10000000         -> 1000000000
dqmul1050 multiply  100    100000000        -> 10000000000
dqmul1051 multiply  100    1000000000       -> 100000000000
dqmul1052 multiply  100    10000000000      -> 1000000000000
dqmul1053 multiply  100    100000000000     -> 10000000000000
dqmul1054 multiply  100    1000000000000    -> 100000000000000
dqmul1055 multiply  100    10000000000000   -> 1000000000000000

dqmul1056 multiply  100    10000000000000000 -> 1000000000000000000
dqmul1057 multiply  100    1000000000000000000000000 -> 100000000000000000000000000
dqmul1058 multiply  100    10000000000000000000000000 -> 1000000000000000000000000000
dqmul1059 multiply  100    100000000000000000000000000 -> 10000000000000000000000000000
dqmul1060 multiply  100    10000000000000000000000000000000 -> 1000000000000000000000000000000000

dqmul1061 multiply  1000   0.01             -> 10.00
dqmul1062 multiply  1000   0.1              -> 100.0
dqmul1063 multiply  1000   1                -> 1000
dqmul1064 multiply  1000   10               -> 10000
dqmul1065 multiply  1000   100              -> 100000
dqmul1066 multiply  1000   1000             -> 1000000
dqmul1067 multiply  1000   10000            -> 10000000
dqmul1068 multiply  1000   100000           -> 100000000
dqmul1069 multiply  1000   1000000          -> 1000000000
dqmul1070 multiply  1000   10000000         -> 10000000000
dqmul1071 multiply  1000   100000000        -> 100000000000
dqmul1072 multiply  1000   1000000000       -> 1000000000000
dqmul1073 multiply  1000   10000000000      -> 10000000000000
dqmul1074 multiply  1000   100000000000     -> 100000000000000
dqmul1075 multiply  1000   1000000000000    -> 1000000000000000

dqmul1076 multiply  1000   1000000000000000 -> 1000000000000000000
dqmul1077 multiply  1000   100000000000000000000000 -> 100000000000000000000000000
dqmul1078 multiply  1000   1000000000000000000000000 -> 1000000000000000000000000000
dqmul1079 multiply  1000   10000000000000000000000000 -> 10000000000000000000000000000
dqmul1080 multiply  1000   1000000000000000000000000000000 -> 1000000000000000000000000000000000

dqmul1081 multiply  10000  0.001            -> 10.000
dqmul1082 multiply  10000  0.01             -> 100.00
dqmul1083 multiply  10000  0.1              -> 1000.0
dqmul1084 multiply  10000  1                -> 10000
dqmul1085 multiply  10000  10               -> 100000
dqmul1086 multiply  10000  100              -> 1000000
dqmul1087 multiply  10000  1000             -> 10000000
dqmul1088 multiply  10000  10000            -> 100000000
dqmul1089 multiply  10000  100000           -> 1000000000
dqmul1090 multiply  10000  1000000          -> 10000000000
dqmul1091 multiply  10000  10000000         -> 100000000000
dqmul1092 multiply  10000  100000000        -> 1000000000000
dqmul1093 multiply  10000  1000000000       -> 10000000000000
dqmul1094 multiply  10000  10000000000      -> 100000000000000
dqmul1095 multiply  10000  100000000000     -> 1000000000000000

dqmul1096 multiply  10000  100000000000000 -> 1000000000000000000
dqmul1097 multiply  10000  10000000000000000000000 -> 100000000000000000000000000
dqmul1098 multiply  10000  100000000000000000000000 -> 1000000000000000000000000000
dqmul1099 multiply  10000  1000000000000000000000000 -> 10000000000000000000000000000
dqmul1100 multiply  10000  100000000000000000000000000000 -> 1000000000000000000000000000000000

dqmul1107 multiply  10000   99999999999     ->  999999999990000
dqmul1108 multiply  10000   99999999999     ->  999999999990000

-- Null tests
dqmul9990 multiply 10  # -> NaN Invalid_operation
dqmul9991 multiply  # 10 -> NaN Invalid_operation

